1. www.cmr.no Interactive computation and visualization of wind farm flow fields based on model reduction Visual Computing Forum 04/11/2011 1 Yngve Heggelund CMR Computing

2. www.cmr.no Visual Computing Forum 04/11/2011 2 Norwegian Centre for Offshore Wind Energy - NORCOWE Center for environment-friendly energy research (CEER) 50% RCN, the rest from industry and research partners Combining Norwegian offshore technology and Danish wind energy competence Research partners: Christian Michelsen Research AS (host) UiS UiA UiB Aalborg University Uni Research AS

3. www.cmr.no NORCOWE WP 4 – Wind farm optimization nVision: Model system for optimizing the layout of (offshore) wind farms based on Computational Fluid Dynamics (CFD) nNowcasting: 2-120 seconds nPower system integration nWind farm modelling Visual Computing Forum 04/11/2011 3

4. www.cmr.no Visual Computing Forum 04/11/2011 4 Wakes nWake effects caused by upstream turbines nReduces energy output of downstream turbines nIncreases material fatigue because of increased turbulence

5. www.cmr.no Visual Computing Forum 04/11/2011 5 Objectives nFind a layout which minimizes the wake effects nReduce the uncertainty of production estimates

6. www.cmr.no Visual Computing Forum 04/11/2011 6 Motivation nTraditional approach: simplified wake models nOften underestimates wake effects nCFD provides the state-of-the-art method for solving complex flow problems nCFD is computationally expensive – one simulation typically takes hours/days/weeks to complete nProhibits straightforward use in optimization of layout nWe have to make some simplifications!

7. www.cmr.no Model reduction, background nIdea: Restrict the solution space to a reduced representative subspace nFull dimension ~3 000 000 grid cells nSubspace dimension ~100 unknowns nE.g. used for real-time visualization of fluid effects (Treuille et al. 2006) nExamples of other applications of model reduction for fluids nStudy of flow past a rectangular cavity (Rowley, 2002) nOptimal rotary control of cylinder wake (Bergman et al., 2005) Visual Computing Forum 04/11/2011 7

8. www.cmr.no Model reduction, theoretical framework Visual Computing Forum 04/11/2011 8

9. www.cmr.no Model reduction, operator examples Visual Computing Forum 04/11/2011 9 CFD discretization Reduced order space representation

10. www.cmr.no Contructing a representative basis nSnapshots of CFD solutions for different placements of turbines nSingular value decomposition (SVD) to extract an orthonormal basis which minimizes the reconstruction error A representative basis is critical for a good result! Visual Computing Forum 04/11/2011 10

11. www.cmr.no Tiles nMust be able to move turbines nConstruct tiles which capture localized behaviour, which can be assembled at runtime nCouple tiles through matching the boundary conditions nResults in a system of equations represented by a large sparse block matrix nSolving for the coefficients in each tile nTrade-off between matching boundary conditions and fulfilling the steady state RANS equations Visual Computing Forum 04/11/2011 11

12. www.cmr.no Test case nIdealized system with three wind turbines and wind predominantly from the west nWhere should turbine C be placed? n6 simulations with FLACS-Wind (CMR GexCon) for different positions of the back row turbine Visual Computing Forum 04/11/2011 12 A B C The two most important modes in the basis

13. www.cmr.no Interactive tool for testing turbine positions nUser can move turbines by dragging tiles nNew flow fields and production estimates are calculated within seconds Visual Computing Forum 04/11/2011 13

14. www.cmr.no Demo Visual Computing Forum 04/11/2011 14